They would like to know if there's a way to add HTML embed code into the HTML view of a piece of content (e.g, discussion, blog post, document are the content types that make most sense to me.)

I last tested this functionality 12 months ago -- when a user asked if it were possible to embed an iFrame. (The answer was: you can embed an iFrame and it will save as a DRAFT but you cannot PUBLISH it.)

To test, I have tried embedding a video into a discussion and a blog post.